the solutions to the following picture. the proof should be similar to what second picture look like,please include how you get each step's reason like the second picture did and don't skip steps please. otherwise please don't answer this

Problem 2. (40 points) (a) (10 points) Let f be a function. Use the standard notation f(z) for the output of f on input r. Express the following statement as a logic formula using quantifiers: f is surjective." (b) (30 points) Prove that composition of two surjective functions f: X Y and g: Y Z is also a surjective function. First write the proof in English and then formalize it using logic (similarly to the notes from 2/132/15 lectures). A direct proof will work here